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Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{1}{5x} + \frac{1}{6y} = 12, \\ \frac{1}{3x} – \frac{3}{7y} = 8 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x} = a,\quad \frac{1}{y} = b \] Then the given equations become: \[ \frac{a}{5} + \frac{b}{6} […]

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{2}{x} + \frac{5}{y} = 1, \\ \frac{60}{x} + \frac{40}{y} = 19 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x} = a,\quad \frac{1}{y} = b \] Then the given equations become: \[ 2a + 5b

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{3}{x} – \frac{1}{y} = -9, \\ \frac{2}{x} + \frac{3}{y} = 5 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x} = a,\quad \frac{1}{y} = b \] Then the given equations become: \[ 3a – b

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{15}{u} + \frac{2}{v} = 17, \\ \frac{1}{u} + \frac{1}{v} = \frac{36}{5} \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{u} = a,\quad \frac{1}{v} = b \] Then the given equations become: \[ 15a + 2b

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{1}{2x} + \frac{1}{3y} = 2, \\ \frac{1}{3x} + \frac{1}{2y} = \frac{13}{6} \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x} = a,\quad \frac{1}{y} = b \] Then the given equations become: \[ \frac{a}{2} + \frac{b}{3}

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{1}{7x} + \frac{1}{6y} = 3, \\ \frac{1}{2x} – \frac{1}{3y} = 5 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x} = a,\quad \frac{1}{y} = b \] Then the given equations become: \[ \frac{a}{7} + \frac{b}{6}

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ 0.5x + 0.7y = 0.74, \\ 0.3x + 0.5y = 0.5 \] Solution Step 1: Remove Decimals Multiply both equations by 10: \[ 5x + 7y = 7.4 \quad \text{(1)} \] \[ 3x + 5y =

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations, where \(y \ne 0\): \[ 2x – \frac{3}{y} = 9, \\ 3x + \frac{7}{y} = 2 \] Solution Step 1: Express One Variable in Terms of the Other From the first equation: \[ 2x – \frac{3}{y} =

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ 3x – \frac{y+7}{11} + 2 = 10, \\ 2y + \frac{x+11}{7} = 10 \] Solution Step 1: Simplify Both Equations First equation: \[ 3x – \frac{y+7}{11} + 2 = 10 \] \[ 3x – \frac{y+7}{11} =

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \sqrt{2}x – \sqrt{3}y = 0, \\ \sqrt{3}x – \sqrt{8}y = 0 \] Solution Step 1: Express One Variable in Terms of the Other From the first equation: \[ \sqrt{2}x – \sqrt{3}y = 0 \] \[ \sqrt{2}x